Tight player raises my bottom two on a draw heavy board

[tightymcfish]

Reads: BB is a tighty player who check raises with big hands (trips,etc) saw him check raise on a JJ9 board with KJ and win a hug pot against KK and J10 in an unraised pot.
Button is a donkey who ive seen cold call before and fold to a turn bet. He probably has a draw of some kind. What is hero's move?
PokerStars No-Limit Hold'em, $2 BB (5 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Hero ($226.30)
BB ($325)
UTG ($68.10)
MP ($431.20)
Button ($215)

Preflop: Hero is SB with 4[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/diamond.gif[/img].
<font color="#666666">2 folds</font>, Button calls $2, Hero completes, BB checks.

Flop: ($6) 8[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 4[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets $4</font>, <font color="#CC3333">BB raises to $10</font>, Button calls $10, Hero???

[Unknown Soldier]

given read I doubt a draw is a big part of his range (which is the only thing you beat). I think this is a fold.

[sixhigh]

Pet pot in the first place. Bet sth like 35 now. Bet 2/3 pot on any safe turn if BB folds. Fold to further resistance.